A unified model for the contact behaviour between equal and dissimilar elastic–plastic spherical bodies

A unified method for calculating the contact force and the contact area between two dissimilar elastic-plastic spheres is presented with the aim of simulating granular materials using particle methods. Explicit equations are presented for the case when the plastic behaviour of the spheres is described with three material parameters. This makes the analysis applicable for a wide range of materials. The model is partly based on dimensionless quantities emerging from the Brinell hardness test. Large deformation of the contact is accounted for in the analysis, which allows for accurate contact relations up to indentation depths relevant for powder compaction. The presented model shows excellent agreement with finite element simulations of two spheres in contact and the results found in literature. An implementation of the contact model in Python is provided together with the online version of this paper.